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Консультация № 159936
08.02.2009, 15:23
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Люди помогите решить задачку она решается както с помощью кругов Эйлера я уже всю голову изломал и ничего не выходит.
Задача: Из 100 человек 85 знают английский язык, 80 – испанский, 75 – немецкий. Сколько человек знают только один язык если все три знают 10 человек?
Задача: Из 100 человек 85 знают английский язык, 80 – испанский, 75 – немецкий. Сколько человек знают только один язык если все три знают 10 человек?
Обсуждение
09.02.2009, 01:58
общий
это ответ
Здравствуйте, Чалпанов Роман Викторович!
Задача не имеет решения!
Пусть большой круг - все 100 человек.
Пусть три малых круга задают людей, которые знают языки.
Причем, зоны, которые на пересечении, задают людей, которые знают два или три языка.
Тогда имеем:
английский язык знают 85 = y (только английский) + a (английский+немецкий) + b (английский+испанский) + 10 (все 3 языка)
немецкий - 75 = x + a + c + 10
испанский - 80 = z + b + c + 10
Сложим три уравнения и получим: x + y + z + 2(a + b + c) = 210 (I)
Теперь сложим все группы людей, в сумме у нас должно получиться ровно 100:
x + y + z + a + b + c + 10 = 100, т.е. x + y + z + a + b + c = 90 (II)
Подставляем в формулу (I) и получаем: a + b + c = 210 - 90 = 120 (III)
Если подставим полученное равенство (III) в формулу (II), то получим невозможное - x + y + z = -30 !!!
Значит, задача решения не имеет (либо ошибка в условии
)
Задача не имеет решения!
Пусть большой круг - все 100 человек.
Пусть три малых круга задают людей, которые знают языки.
Причем, зоны, которые на пересечении, задают людей, которые знают два или три языка.
Тогда имеем:
английский язык знают 85 = y (только английский) + a (английский+немецкий) + b (английский+испанский) + 10 (все 3 языка)
немецкий - 75 = x + a + c + 10
испанский - 80 = z + b + c + 10
Сложим три уравнения и получим: x + y + z + 2(a + b + c) = 210 (I)
Теперь сложим все группы людей, в сумме у нас должно получиться ровно 100:
x + y + z + a + b + c + 10 = 100, т.е. x + y + z + a + b + c = 90 (II)
Подставляем в формулу (I) и получаем: a + b + c = 210 - 90 = 120 (III)
Если подставим полученное равенство (III) в формулу (II), то получим невозможное - x + y + z = -30 !!!
Значит, задача решения не имеет (либо ошибка в условии
)
Об авторе:
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
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